Preheat the oven to 400 degrees.
Heat the olive oil in a large skillet over medium high heat. Add the chicken and cook until browned, about 4 minutes per side. Transfer to a cutting board. Allow to stand for 5 minutes then cut into 1 inch pieces.
In a small bowl combine the flour and 1 cup of milk. Whisk until smooth.
Add the milk and chicken broth to the skillet. Bring to a boil over medium high heat.
Gradually whisk in the flour milk mixture. Return to a boil and cook, stirring frequently, until thickened.
Stir in rice, broccoli, onion, and garlic. Return to a boil and cook for 3-4 minutes.
Stir in the chicken, cheese, salt, pepper, and thyme.
Pour the chicken and rice mixture into a baking dish. Top with crispy fried onions.
Bake for 20 minutes or until the casserole is bubbling.
Remove from oven and cool for 5 minutes.